Research Methodology - Dr. Krishan K. Pandey
Research Methodology - Dr. Krishan K. Pandey Research Methodology - Dr. Krishan K. Pandey
Measurement and Scaling Techniques 69 5 Measurement and Scaling Techniques MEASUREMENT IN RESEARCH In our daily life we are said to measure when we use some yardstick to determine weight, height, or some other feature of a physical object. We also measure when we judge how well we like a song, a painting or the personalities of our friends. We, thus, measure physical objects as well as abstract concepts. Measurement is a relatively complex and demanding task, specially so when it concerns qualitative or abstract phenomena. By measurement we mean the process of assigning numbers to objects or observations, the level of measurement being a function of the rules under which the numbers are assigned. It is easy to assign numbers in respect of properties of some objects, but it is relatively difficult in respect of others. For instance, measuring such things as social conformity, intelligence, or marital adjustment is much less obvious and requires much closer attention than measuring physical weight, biological age or a person’s financial assets. In other words, properties like weight, height, etc., can be measured directly with some standard unit of measurement, but it is not that easy to measure properties like motivation to succeed, ability to stand stress and the like. We can expect high accuracy in measuring the length of pipe with a yard stick, but if the concept is abstract and the measurement tools are not standardized, we are less confident about the accuracy of the results of measurement. Technically speaking, measurement is a process of mapping aspects of a domain onto other aspects of a range according to some rule of correspondence. In measuring, we devise some form of scale in the range (in terms of set theory, range may refer to some set) and then transform or map the properties of objects from the domain (in terms of set theory, domain may refer to some other set) onto this scale. For example, in case we are to find the male to female attendance ratio while conducting a study of persons who attend some show, then we may tabulate those who come to the show according to sex. In terms of set theory, this process is one of mapping the observed physical properties of those coming to the show (the domain) on to a sex classification (the range). The rule of correspondence is: If the object in the domain appears to be male, assign to “0” and if female assign to “1”. Similarly, we can record a person’s marital status as 1, 2, 3 or 4, depending on whether
70 Research Methodology the person is single, married, widowed or divorced. We can as well record “Yes or No” answers to a question as “0” and “1” (or as 1 and 2 or perhaps as 59 and 60). In this artificial or nominal way, categorical data (qualitative or descriptive) can be made into numerical data and if we thus code the various categories, we refer to the numbers we record as nominal data. Nominal data are numerical in name only, because they do not share any of the properties of the numbers we deal in ordinary arithmetic. For instance if we record marital status as 1, 2, 3, or 4 as stated above, we cannot write 4 > 2 or 3 < 4 and we cannot write 3 – 1 = 4 – 2, 1 + 3 = 4 or 4 ÷ 2 = 2. In those situations when we cannot do anything except set up inequalities, we refer to the data as ordinal data. For instance, if one mineral can scratch another, it receives a higher hardness number and on Mohs’ scale the numbers from 1 to 10 are assigned respectively to talc, gypsum, calcite, fluorite, apatite, feldspar, quartz, topaz, sapphire and diamond. With these numbers we can write 5 > 2 or 6 < 9 as apatite is harder than gypsum and feldspar is softer than sapphire, but we cannot write for example 10 – 9 = 5 – 4, because the difference in hardness between diamond and sapphire is actually much greater than that between apatite and fluorite. It would also be meaningless to say that topaz is twice as hard as fluorite simply because their respective hardness numbers on Mohs’ scale are 8 and 4. The greater than symbol (i.e., >) in connection with ordinal data may be used to designate “happier than” “preferred to” and so on. When in addition to setting up inequalities we can also form differences, we refer to the data as interval data. Suppose we are given the following temperature readings (in degrees Fahrenheit): 58°, 63°, 70°, 95°, 110°, 126° and 135°. In this case, we can write 100° > 70° or 95° < 135° which simply means that 110° is warmer than 70° and that 95° is cooler than 135°. We can also write for example 95° – 70° = 135° – 110°, since equal temperature differences are equal in the sense that the same amount of heat is required to raise the temperature of an object from 70° to 95° or from 110° to 135°. On the other hand, it would not mean much if we said that 126° is twice as hot as 63°, even though 126° ÷ 63° = 2. To show the reason, we have only to change to the centigrade scale, where the first temperature becomes 5/9 (126 – 32) = 52°, the second temperature becomes 5/9 (63 – 32) = 17° and the first figure is now more than three times the second. This difficulty arises from the fact that Fahrenheit and Centigrade scales both have artificial origins (zeros) i.e., the number 0 of neither scale is indicative of the absence of whatever quantity we are trying to measure. When in addition to setting up inequalities and forming differences we can also form quotients (i.e., when we can perform all the customary operations of mathematics), we refer to such data as ratio data. In this sense, ratio data includes all the usual measurement (or determinations) of length, height, money amounts, weight, volume, area, pressures etc. The above stated distinction between nominal, ordinal, interval and ratio data is important for the nature of a set of data may suggest the use of particular statistical techniques * . A researcher has to be quite alert about this aspect while measuring properties of objects or of abstract concepts. * When data can be measured in units which are interchangeable e.g., weights (by ratio scales), temperatures (by interval scales), that data is said to be parametric and can be subjected to most kinds of statistical and mathematical processes. But when data is measured in units which are not interchangeable, e.g., product preferences (by ordinal scales), the data is said to be non-parametric and is susceptible only to a limited extent to mathematical and statistical treatment.
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Measurement and Scaling Techniques 69<br />
5<br />
Measurement and Scaling<br />
Techniques<br />
MEASUREMENT IN RESEARCH<br />
In our daily life we are said to measure when we use some yardstick to determine weight, height, or<br />
some other feature of a physical object. We also measure when we judge how well we like a song,<br />
a painting or the personalities of our friends. We, thus, measure physical objects as well as abstract<br />
concepts. Measurement is a relatively complex and demanding task, specially so when it concerns<br />
qualitative or abstract phenomena. By measurement we mean the process of assigning numbers to<br />
objects or observations, the level of measurement being a function of the rules under which the<br />
numbers are assigned.<br />
It is easy to assign numbers in respect of properties of some objects, but it is relatively difficult in<br />
respect of others. For instance, measuring such things as social conformity, intelligence, or marital<br />
adjustment is much less obvious and requires much closer attention than measuring physical weight,<br />
biological age or a person’s financial assets. In other words, properties like weight, height, etc., can<br />
be measured directly with some standard unit of measurement, but it is not that easy to measure<br />
properties like motivation to succeed, ability to stand stress and the like. We can expect high accuracy<br />
in measuring the length of pipe with a yard stick, but if the concept is abstract and the measurement<br />
tools are not standardized, we are less confident about the accuracy of the results of measurement.<br />
Technically speaking, measurement is a process of mapping aspects of a domain onto other<br />
aspects of a range according to some rule of correspondence. In measuring, we devise some form of<br />
scale in the range (in terms of set theory, range may refer to some set) and then transform or map the<br />
properties of objects from the domain (in terms of set theory, domain may refer to some other set)<br />
onto this scale. For example, in case we are to find the male to female attendance ratio while<br />
conducting a study of persons who attend some show, then we may tabulate those who come to the<br />
show according to sex. In terms of set theory, this process is one of mapping the observed physical<br />
properties of those coming to the show (the domain) on to a sex classification (the range). The rule<br />
of correspondence is: If the object in the domain appears to be male, assign to “0” and if female<br />
assign to “1”. Similarly, we can record a person’s marital status as 1, 2, 3 or 4, depending on whether
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